FRANKFURT, Germany (AP) ― Twenty-one months after Greece triggered financial and political turmoil by admitting it was broke, the eurozone still can’t fix its debt crisis.

The reasons: intractable disputes over who will ultimately pay the costs of saving it, and the still-unadressed vulnerability that comes from having a single currency with multiple governments.

One after another, troubled European countries have asked for bailouts: Greece, Ireland, Portugal. Late-night meetings produced hasty statements and new crisis measures, like Sunday’s rushed decision by the European Central Bank to buy Spanish and Italian bonds and ward off financial collapse there. Bond markets steadied, but by midweek the cloud of fear simply moved to France, with panic selling of French bank stocks.

The 17 countries who must solve the crisis remain deeply divided over how to distribute the potentially astronomical costs of available fixes.

It took months, for instance, to reach agreement on a relatively modest reduction in Greece’s debt by persuading bondholders to take less than 100 cents on the euro.

As a result, expect more debate and more crisis headlines.

The basic problem is simple: Some of the euro countries have too much debt. Markets wonder if they can pay it back. As a result, lenders are demanding interest rates that would quickly grind government budgets down to insolvency, in a self-fulfilling death spiral.

But how to fix that problem is far from straightforward. Much depends on the answers; the euro debt crisis poses a serious risk for an economy that, taken as a whole, ranks behind only the United States in size and remains a major trade partner for the U.S. and China. The turmoil has sent stocks down and fed fears over global growth just as the U.S. debt dispute did.

The fractures go back to the creation of the euro in 1999, as a stable currency with low inflation and interest rates, but no effective way t o restrain multiple legislatures from undermining that with too much spending.

Joining meant smaller countries could suddenly borrow almost as cheaply as solid industrial giant Germany. At the time, that was celebrated as a major achievement. Less money for interest payments, more for schools and roads. But some countries, notoriously Greece, misused the unaccustomed access to cheap credit, paying for a bigger government with lots of jobs to give people.

As they did that, wages and prices rose, making the economy less efficient. Credit flooded into Spain and Ireland for real estate booms. Lenders went along. They assumed euro membership meant nothing could go wrong.

Some had seen the danger, however. The EU wrote rules to limit debt and deficits. But eurozone heavyweights France and Germany later tore them up when they wanted to run deficits over the limit of 3 percent of gross domestic product.

The complacency ended in late 2009, when Greece admitted its finances were much worse than official statistics had shown. Default fears sent interest rates soaring and left Greece ― and two other indebted countries, Ireland and Portugal, unable to pay.

To avoid the disruption of a default, they were rescued by hastily arranged bailout loans ― Greece euro110 and then again euro109 billion, Ireland euro67.5 billion, Portugal euro78 billion ― from the other eurozone countries and the International Monetary Fund.

Now Germany and other financially solid countries, afraid of compromising their own finances to help others, are balking at putting more money in the European Union’s rescue fund, saying euro440 billion is enough. Yet that is clearly too small to rescue a larger country such as Italy, which would need euro665 billion to stay afloat for three years, and which has dangerous levels of debt.

Meanwhile, indebted countries have tried the obvious: reduce debt by cutting spending. But the spending cuts make economies shrink. The debt gets bigger, not smaller.

Greece has been cutting like mad, but its debt is rising toward 160 percent of economic output, behind only Japan among rich countries.

Countries could default, the way poorer nations have for years, often giving creditors half what they’re owed, or less. Greece is in effect doing a modest version of that, asking investors to take new bonds worth 21 percent less.

But bigger defaults risk shattering Europe’s banks, which are major bondholders. As with the Lehman Brothers bankruptcy in 2008, a government default could inflict such heavy losses on banks that they choke off credit to everyone ― businesses and consumers too. Result: deep recession.

Indebted countries could leave the euro, default and then devalue their currencies to shrink debt. But the chaos and costs would be so extreme and unpredictable that everything else will likely be tried first.

One fix that is frequently discussed by economists is eurobonds, or jointly backed borrowing.

Pooled responsibility from all eurozone countries would mean no one could have trouble paying. Lenders would make affordable credit available.

But Germany, the eurozone’s political and financial heavyweight, once again says no.

Germany borrows cheaply because of its big economy and stronger finances, after painful cuts in social benefits and an increase in the retirement age to 67.

A eurobond’s averaged-out interest rate could mean higher borrowing costs for Germany, meaning less to spend on schools, pensions and roads ― but lower costs for less disciplined Italy, Greece, Spain, Portugal, Ireland.

In essence, the euro would become a “transfer union.” Germans would transfer money to others and see their risks transferred to it. So far it’s politically unacceptable in Germany.

As a partial fix, stronger defict rules have been drawn up, but even now there are arguments about whether penalties on violators should be automatic ― or left, as before, ultimately in the hands of politicians.

European Central Bank President Jean-Claude Trichet proposes a eurozone finance ministry that could veto government spending. But that would take years to put in place. And there’s no clear way to make that post accountable to voters ― to avoid the charge of taxation without representation.